It has been deemed desirable in certain liquid dispensing applications to increase the flow rate at which a beverage or other liquid or flowable food product or other flowable substance, such as condiments or the like, are dispensed from a faucet. Examples of such applications are fast-food operations or sports or other entertainment concession stands where speed of customer service is critical. At the same time, it has also been deemed desirable to provide a high-flow faucet that operates in a one-handed and otherwise simple manner. As such, a need has been identified for a liquid dispensing faucet that increases the flow rate of liquid being dispensed while also being easily controlled in a one-handed manner. Another need has been identified for a faucet that can be operated with one hand and that facilitates mixing of liquids or other flowable products from two separate sources only at the time when the liquids are dispensed into an associated cup or other container.